Prove that 2 + 5 + 8...+ (3n -1) = (1/2)n(3n+1) for all n N.
Seems to only work for the base case. Can this be proved by induction?
Another way to write this is as follows:
Prove that
To prove this by induction, see if it works for the base case of
, thus base case holds.
The next step is to ASSUME the rule holds for k. Take it for granted that:
Now, using this result, try to prove that the rule also holds for k+1.
Here's a tip: